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Geometry of Continued Fractions

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Cover of 'Geometry of Continued Fractions'

Table of Contents

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    Book Overview
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    Chapter 1 Classical Notions and Definitions
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    Chapter 2 On Integer Geometry
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    Chapter 3 Geometry of Regular Continued Fractions
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    Chapter 4 Complete Invariant of Integer Angles
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    Chapter 5 Integer Trigonometry for Integer Angles
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    Chapter 6 Integer Angles of Integer Triangles
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    Chapter 7 Continued Fractions and $\operatorname{SL}(2,{\mathbb{Z}})$ Conjugacy Classes. Elements of Gauss’s Reduction Theory. Markov Spectrum
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    Chapter 8 Lagrange’s Theorem
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    Chapter 9 Gauss–Kuzmin Statistics
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    Chapter 10 Geometric Aspects of Approximation
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    Chapter 11 Geometry of Continued Fractions with Real Elements and Kepler’s Second Law
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    Chapter 12 Extended Integer Angles and Their Summation
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    Chapter 13 Integer Angles of Polygons and Global Relations for Toric Singularities
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    Chapter 14 Basic Notions and Definitions of Multidimensional Integer Geometry
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    Chapter 15 On Empty Simplices, Pyramids, Parallelepipeds
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    Chapter 16 Multidimensional Continued Fractions in the Sense of Klein
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    Chapter 17 Dirichlet Groups and Lattice Reduction
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    Chapter 18 Periodicity of Klein Polyhedra. Generalization of Lagrange’s Theorem
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    Chapter 19 Multidimensional Gauss–Kuzmin Statistics
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    Chapter 20 On Construction of Multidimensional Continued Fractions
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    Chapter 21 Gauss Reduction in Higher Dimensions
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    Chapter 22 Approximation of Maximal Commutative Subgroups
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    Chapter 23 Other Generalizations of Continued Fractions
Attention for Chapter 13: Integer Angles of Polygons and Global Relations for Toric Singularities
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Chapter title
Integer Angles of Polygons and Global Relations for Toric Singularities
Chapter number 13
Book title
Geometry of Continued Fractions
Published by
Springer, Berlin, Heidelberg, January 2013
DOI 10.1007/978-3-642-39368-6_13
Book ISBNs
978-3-64-239367-9, 978-3-64-239368-6
Authors

Oleg Karpenkov